Growth of symbolic number knowledge accelerates after children understand cardinality.

Children who achieve an early understanding of the cardinal value of number words (cardinal knowledge) have a superior understanding of the relations among numerals at school entry, controlling other factors (e.g., intelligence). We tested the hypothesis that this pattern emerges because an understanding of cardinal value jump starts children's learning of the relations among numerals. Across two years of preschool, the cardinal knowledge of 179 children (85 boys) was assessed four times, as was their understanding of the relative quantity of Arabic numerals and competence at discriminating nonsymbolic quantities. Children were more accurate on nonsymbolic than numeral comparisons before they understood cardinality, but showed more rapid growth for numeral than nonsymbolic comparisons once they understood cardinality. Moreover, and with the possible exception of very small numerals (<5), before they understood cardinality children were no better than chance in their numeral comparisons, but greatly exceeded chance once they understood cardinality. These patterns were independent of the age at which children became cardinal principle knowers and independent of intelligence, executive function, and preliteracy skills. More broadly, the results provide a developmental bridge between cardinal knowledge and school-entry number knowledge.